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Field experiment was conducted during the three consecutive cropping seasons (2017-2018, 2018-2019 and 2019-2020) at the experimental field of ITGC, Setif, Algeria to study the selection of adapted and stable genotypes of triticale based on the use of some parametric and non-parametric index. The program STABILITYSOFT was used to calculate the parametric and non-parametric index. The graphic distribution of the genotypes tested based on the relationship between the mean grain yield and regression coefficient (bi), proved that the suitable genotypes for the tested conditions are G2, and G3. The association between Wricke'secovalence (Wi²), the coefficient of variance (CVi), the mean variance component (θi) and the Stability variance (σ²i) indices with the grain yield proved that the best genotypes for growing under these conditions were G2 and G3.In addition, the selection based on the non-parametric index showed that the genotypes G1, G2 and G3 were the most stables. The combination selection based on highest grain yield and the parametric indices proved that the genotypes G2 and G3 are the more stable and more adapted under semi-arid conditions. The results of spearman's rank correlation and PCA analysis for grouping the different parametric stability statistics studied showed that stability indices could be classified into four groups. Moreover, and based on the static and dynamic concepts, the parametric indices bi and CVi are related to the static concept, while the other indices were associated with dynamic stability concept. Overall, the results of this study confirmed that the parametric and non-parametric methods were the suitable tools to identify the most stable triticale genotypes at various environmental conditions. [ABSTRACT FROM AUTHOR]